箱形图

用matplotlib可视化箱形图。

以下示例展示了如何使用Matplotlib可视化箱图。有许多选项可以控制它们的外观以及用于汇总数据的统计信息。

  1. import matplotlib.pyplot as plt
  2. import numpy as np
  3. from matplotlib.patches import Polygon
  6. # Fixing random state for reproducibility
  7. np.random.seed(19680801)
  9. # fake up some data
  10. spread = np.random.rand(50) * 100
  11. center = np.ones(25) * 50
  12. flier_high = np.random.rand(10) * 100 + 100
  13. flier_low = np.random.rand(10) * -100
  14. data = np.concatenate((spread, center, flier_high, flier_low))
  16. fig, axs = plt.subplots(2, 3)
  18. # basic plot
  19. axs[0, 0].boxplot(data)
  20. axs[0, 0].set_title('basic plot')
  22. # notched plot
  23. axs[0, 1].boxplot(data, 1)
  24. axs[0, 1].set_title('notched plot')
  26. # change outlier point symbols
  27. axs[0, 2].boxplot(data, 0, 'gD')
  28. axs[0, 2].set_title('change outlier\npoint symbols')
  30. # don't show outlier points
  31. axs[1, 0].boxplot(data, 0, '')
  32. axs[1, 0].set_title("don't show\noutlier points")
  34. # horizontal boxes
  35. axs[1, 1].boxplot(data, 0, 'rs', 0)
  36. axs[1, 1].set_title('horizontal boxes')
  38. # change whisker length
  39. axs[1, 2].boxplot(data, 0, 'rs', 0, 0.75)
  40. axs[1, 2].set_title('change whisker length')
  42. fig.subplots_adjust(left=0.08, right=0.98, bottom=0.05, top=0.9,
  43.                     hspace=0.4, wspace=0.3)
  45. # fake up some more data
  46. spread = np.random.rand(50) * 100
  47. center = np.ones(25) * 40
  48. flier_high = np.random.rand(10) * 100 + 100
  49. flier_low = np.random.rand(10) * -100
  50. d2 = np.concatenate((spread, center, flier_high, flier_low))
  51. data.shape = (-1, 1)
  52. d2.shape = (-1, 1)
  53. # Making a 2-D array only works if all the columns are the
  54. # same length.  If they are not, then use a list instead.
  55. # This is actually more efficient because boxplot converts
  56. # a 2-D array into a list of vectors internally anyway.
  57. data = [data, d2, d2[::2, 0]]
  59. # Multiple box plots on one Axes
  60. fig, ax = plt.subplots()
  61. ax.boxplot(data)
  63. plt.show()

下面我们将从五个不同的概率分布生成数据，每个概率分布具有不同的特征。 我们想要了解数据的IID引导程序重采样如何保留原始样本的分布属性，并且箱形图是进行此评估的一种可视化工具。

  1. numDists = 5
  2. randomDists = ['Normal(1,1)', ' Lognormal(1,1)', 'Exp(1)', 'Gumbel(6,4)',
  3.                'Triangular(2,9,11)']
  4. N = 500
  6. norm = np.random.normal(1, 1, N)
  7. logn = np.random.lognormal(1, 1, N)
  8. expo = np.random.exponential(1, N)
  9. gumb = np.random.gumbel(6, 4, N)
  10. tria = np.random.triangular(2, 9, 11, N)
  12. # Generate some random indices that we'll use to resample the original data
  13. # arrays. For code brevity, just use the same random indices for each array
  14. bootstrapIndices = np.random.random_integers(0, N - 1, N)
  15. normBoot = norm[bootstrapIndices]
  16. expoBoot = expo[bootstrapIndices]
  17. gumbBoot = gumb[bootstrapIndices]
  18. lognBoot = logn[bootstrapIndices]
  19. triaBoot = tria[bootstrapIndices]
  21. data = [norm, normBoot, logn, lognBoot, expo, expoBoot, gumb, gumbBoot,
  22.         tria, triaBoot]
  24. fig, ax1 = plt.subplots(figsize=(10, 6))
  25. fig.canvas.set_window_title('A Boxplot Example')
  26. fig.subplots_adjust(left=0.075, right=0.95, top=0.9, bottom=0.25)
  28. bp = ax1.boxplot(data, notch=0, sym='+', vert=1, whis=1.5)
  29. plt.setp(bp['boxes'], color='black')
  30. plt.setp(bp['whiskers'], color='black')
  31. plt.setp(bp['fliers'], color='red', marker='+')
  33. # Add a horizontal grid to the plot, but make it very light in color
  34. # so we can use it for reading data values but not be distracting
  35. ax1.yaxis.grid(True, linestyle='-', which='major', color='lightgrey',
  36.                alpha=0.5)
  38. # Hide these grid behind plot objects
  39. ax1.set_axisbelow(True)
  40. ax1.set_title('Comparison of IID Bootstrap Resampling Across Five Distributions')
  41. ax1.set_xlabel('Distribution')
  42. ax1.set_ylabel('Value')
  44. # Now fill the boxes with desired colors
  45. boxColors = ['darkkhaki', 'royalblue']
  46. numBoxes = numDists*2
  47. medians = list(range(numBoxes))
  48. for i in range(numBoxes):
  49.     box = bp['boxes'][i]
  50.     boxX = []
  51.     boxY = []
  52.     for j in range(5):
  53.         boxX.append(box.get_xdata()[j])
  54.         boxY.append(box.get_ydata()[j])
  55.     boxCoords = np.column_stack([boxX, boxY])
  56.     # Alternate between Dark Khaki and Royal Blue
  57.     k = i % 2
  58.     boxPolygon = Polygon(boxCoords, facecolor=boxColors[k])
  59.     ax1.add_patch(boxPolygon)
  60.     # Now draw the median lines back over what we just filled in
  61.     med = bp['medians'][i]
  62.     medianX = []
  63.     medianY = []
  64.     for j in range(2):
  65.         medianX.append(med.get_xdata()[j])
  66.         medianY.append(med.get_ydata()[j])
  67.         ax1.plot(medianX, medianY, 'k')
  68.         medians[i] = medianY[0]
  69.     # Finally, overplot the sample averages, with horizontal alignment
  70.     # in the center of each box
  71.     ax1.plot([np.average(med.get_xdata())], [np.average(data[i])],
  72.              color='w', marker='*', markeredgecolor='k')
  74. # Set the axes ranges and axes labels
  75. ax1.set_xlim(0.5, numBoxes + 0.5)
  76. top = 40
  77. bottom = -5
  78. ax1.set_ylim(bottom, top)
  79. ax1.set_xticklabels(np.repeat(randomDists, 2),
  80.                     rotation=45, fontsize=8)
  82. # Due to the Y-axis scale being different across samples, it can be
  83. # hard to compare differences in medians across the samples. Add upper
  84. # X-axis tick labels with the sample medians to aid in comparison
  85. # (just use two decimal places of precision)
  86. pos = np.arange(numBoxes) + 1
  87. upperLabels = [str(np.round(s, 2)) for s in medians]
  88. weights = ['bold', 'semibold']
  89. for tick, label in zip(range(numBoxes), ax1.get_xticklabels()):
  90.     k = tick % 2
  91.     ax1.text(pos[tick], top - (top*0.05), upperLabels[tick],
  92.              horizontalalignment='center', size='x-small', weight=weights[k],
  93.              color=boxColors[k])
  95. # Finally, add a basic legend
  96. fig.text(0.80, 0.08, str(N) + ' Random Numbers',
  97.          backgroundcolor=boxColors[0], color='black', weight='roman',
  98.          size='x-small')
  99. fig.text(0.80, 0.045, 'IID Bootstrap Resample',
  100.          backgroundcolor=boxColors[1],
  101.          color='white', weight='roman', size='x-small')
  102. fig.text(0.80, 0.015, '*', color='white', backgroundcolor='silver',
  103.          weight='roman', size='medium')
  104. fig.text(0.815, 0.013, ' Average Value', color='black', weight='roman',
  105.          size='x-small')
  107. plt.show()

箱形图

在这里，我们编写一个自定义函数来引导置信区间。然后我们可以使用boxplot和此函数来显示这些间隔。

  1. def fakeBootStrapper(n):
  2.     '''
  3.     This is just a placeholder for the user's method of
  4.     bootstrapping the median and its confidence intervals.
  6.     Returns an arbitrary median and confidence intervals
  7.     packed into a tuple
  8.     '''
  9.     if n == 1:
  10.         med = 0.1
  11.         CI = (-0.25, 0.25)
  12.     else:
  13.         med = 0.2
  14.         CI = (-0.35, 0.50)
  16.     return med, CI
  18. inc = 0.1
  19. e1 = np.random.normal(0, 1, size=(500,))
  20. e2 = np.random.normal(0, 1, size=(500,))
  21. e3 = np.random.normal(0, 1 + inc, size=(500,))
  22. e4 = np.random.normal(0, 1 + 2*inc, size=(500,))
  24. treatments = [e1, e2, e3, e4]
  25. med1, CI1 = fakeBootStrapper(1)
  26. med2, CI2 = fakeBootStrapper(2)
  27. medians = [None, None, med1, med2]
  28. conf_intervals = [None, None, CI1, CI2]
  30. fig, ax = plt.subplots()
  31. pos = np.array(range(len(treatments))) + 1
  32. bp = ax.boxplot(treatments, sym='k+', positions=pos,
  33.                 notch=1, bootstrap=5000,
  34.                 usermedians=medians,
  35.                 conf_intervals=conf_intervals)
  37. ax.set_xlabel('treatment')
  38. ax.set_ylabel('response')
  39. plt.setp(bp['whiskers'], color='k', linestyle='-')
  40. plt.setp(bp['fliers'], markersize=3.0)
  41. plt.show()

箱形图2

下载这个示例